MATHEMATICAL-ANALYSIS OF A MODEL FOR NUCLEAR-REACTOR DYNAMICS

In this paper we study the global existence; asymptotic behavior, and blowing-up property of solutions of the initial-boundary value problem for the nonlinear integrodifferential reaction-diffusion equation u(1 ) + Lu = lambda u + mu u integral(0)(t) u(x, s) ds, with L a uniformly elliptic, self-adjoint operator, which arises in nuclear reactor dyna mics. The estimates of asymptotic behavior and escape time given here are optimal in a sense. In particular, we find that if mu < 0 then the solution exists globally and diminishes to the steady-state solution u = 0 faster than any exponential function e(-alpha t) (a > 0) does. I f mu > 0, lambda < 0, L = - (partial derivative/partial derivative x(i )) (alpha(ij)(x) (partial derivative/partial derivative x(j))) and the boundary condition is Neumann condition, then the solution may tend t o zero as t --> +infinity or blow up in finite time depending on the i nitial Value less than or equal to lambda(2)/2 mu or > lambda(2)/2 mu. (C) 1994 Academic Press, Inc.